Transp Porous Med DOI 10.1007/s11242-012-0080-3 A Note on Local Thermal Non-equilibrium in Porous Media and Heat Flux Bifurcation Phenomenon in Porous Media Kambiz Vafai · Kun Yang Received: 20 September 2012 / Accepted: 21 September 2012 © Springer Science+Business Media Dordrecht 2012 Abstract This work address a number of fundamental issues and concepts related to local thermal non-equilibrium and the heat flux bifurcation phenomenon in porous media. Differ- ent types of heat flux bifurcation phenomenon are discussed in relation to previous works by the authors. Keywords Local thermal non-equilibrium · Heat flux bifurcation phenomenon · Porous media We appreciate the interest expressed by Nield (2012) for recognizing the importance of the heat flux bifurcation phenomena, which was first, discovered and analyzed by Yang and Vafai (2010, 2011a, b). While we appreciate the effort put forth by Nield (2012) to high- light our work in the bifurcation area, his work (Nield 2012) carries a number of inaccurate statements. The work of Yang and Vafai (2010) was one of the first attempts to study the heat flux bifurcation phenomenon in porous media under local thermal non-equilibrium (LTNE) con- dition. The exact solutions for both the fluid and solid temperature distributions for convective heat transfer within a channel fully filled with a porous medium subject to a constant wall heat flux boundary condition, with internal heat generation in both the fluid and solid phases, were obtained. In the work of Yang and Vafai (2010), the “heat flux bifurcation phenomenon” indicates that the direction of the temperature gradient for the fluid and solid phases are dif- ferent at the wall. They also derived the necessary conditions for heat flux bifurcation. Yang and Vafai (2011a) demonstrated the existence of two primary types of heat flux bifurcations at the wall under temporal conditions. The first type is the same as the one discussed by K. Vafai (B) Department of Mechanical Engineering, University of California, Riverside, CA 92691, USA e-mail: vafai@engr.ucr.edu K. Yang School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China 123